28D matter waves, uncertainty - 5/22/2011 Outline Physics...

5/22/20111Physics 1CLecture 28D"I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars."--Sir Arthur EddingtonOutlineAn Interpretation of QMParticle in a box Atomic physicsEmission spectraAbsorption spectra An Interpretation of QMProbabilityVNIV2IEParticle interpretation: Wave interpretation: the intensity is proportional to the square of the electric field amplitude: 2ProbabilityVECombine the two points of view: For EM radiation, the probability of finding a particle associated with this radiation is proportional to the square of the amplitude of the associated EM wave.The particle is the photon in this case.The amplitude of the wave is called the probability amplitudeor the wave function. The symbol is y.An Interpretation of QMThe probabilistic interpretation of the wave function was suggested by Max Born in 1928.Erwin Schrödinger proposed a wave equation which describes the manner in which the wave function changes in space and evolves with time.This equation is a key element in the theory of quantum mechanics.If represents a single particle, ||2is the relative probability per unit volume that the particle will be found at any given point in the volume.||2is called the probability density.Particle in a BoxLet’s consider a particle confined to a one-dimensional region in space.Following the quantum mechanics approach, we need to find an appropriate wave function to describe the motion of the particle.Because of the walls, the probability of finding the particle outside the box is zero.This means that (x)=0for x0 and for xL.When the particle is inside the box, the potential energy of the system is constant.Particle in a Box2( )sinxxA=We can define the potential energy to be infinitely large outside the box.

This preview
has intentionally blurred sections.
Sign up to view the full version.